Critical Behavior in the Rotating D-branes

TL;DR

The paper investigates phase transitions in the dual conformal field theories living on rotating D3-, M5-, and M2-branes by analyzing the thermodynamics of their rotating black-brane solutions in both grand canonical and canonical ensembles. It identifies stability boundaries in angular momentum density, computes critical exponents for thermodynamic quantities, and derives correlation-function exponents tied to worldvolume dimensions, finding a set of largely universal values for the exponents. The results show ensemble-dependent shifts of the critical points and Hawking-Page transitions, with no HP in the grand canonical ensemble and possible HP behavior in the canonical for D3- and M5-branes, while M2-branes show no critical point in either ensemble. The work emphasizes the role of R-charge in driving phase structure and highlights potential universality across brane systems, as well as the non-equivalence of thermodynamic ensembles in these self-gravitating backgrounds.

Abstract

The low energy excitation of the rotating D3-branes is thermodynamically stable up to a critical angular momentum density. This indicates that there is a corresponding phase transition of the ${\cal N}$=4 large $N$ super Yang-Mills theory at finite temperature. On the side of supergravity, we investigate the phase transition in the grand canonical ensemble and canonical ensemble. Some critical exponents of thermodynamic quantities are calculated. They obey the static scaling laws. Using the scaling laws related to the correlation length, we get the critical exponents of the correlation function of gauge field. The thermodynamic stability of low energy excitations of the rotating M5-branes and rotating M2-branes is also studied and similar critical behavior is observed. We find that the critical point is shifted in the different ensembles and there is no critical point in the canonical ensemble for the rotating M2-branes. We also discuss the Hawking-Page transition for these rotating branes. In the grand canonical ensemble, the Hawking-Page transition does not occur. In the canonical ensemble, however, the Hawking-Page transition may appear for the rotating D3- and M5-branes, but not for the rotating M2-branes.